I'm about to start playing FFXI for the first time in like 6 years(initial release on ps2, only got to the dunes though..) with a brand spanking new account. What the best way to go about getting a flexible dragoon. I was thinking of leveling monk to 18, warrior to 30, hopefully get some help with DRG line. I was thinking after that try to go between DRG/WAR (eventually DRG/SAM) and DRG/BLU. Is this a good idea or is there a better way?

The best way is to just have multiple subjobs unlocked and leveled up, so that you'll always have that flexibility available to you. In situations where you're just there to be a DD, /War and /Sam are going to be your bread and butter subjobs, especially /Sam when you can work your way down to a 5-hit build with proper gear. In more solo oriented or low-man situations, Restorative Breath and its 1 minute timer may not be enough, so having some form of /mage is going to be useful.

In some situations I was/am more partial to using /Rdm, since the elemental Bar- spells have extremely short cast times, cost little MP, you have 6 of them so at least one is always going to be up for triggering Healing Breath, and since they're self-target, you don't need to be fighting anything to get it to go off. /Blu offers a few similarly short cast/recast time/MP cost spells (Power Attack and Foot Kick) and a great defense spell in Cocoon, but their downside is what I mentioned above when talking about Red Mage. Their cheapest spells need to be cast on targets, so it takes a bit more time/MP to cure yourself up when not fighting, because you'll need to use some of the more expensive, slow casting spells to trigger Healing Breath.

It's really just good to have a number of SJ available so that you have that flexibility to do whatever you need to come about.